How to merge a bunch of objects into one?
There are several possible problems that cause the faces to disappear in Unity. The way Unity calculates normal is usually by hiding all of the weird angled faces and flipped normals. So try to:


Select every vertices in Edit Mode and hit 'W' to bring up Special Menu. Choose Remove Doubles to merge every overlapping vertices at the same position.
In Edit Mode, this time with nothing selected, you hit 'Spacebar' and then type in 'Select faces by sides', hit enter. Then hit F6 on keyboard to edit the Properties. Choose 'Number of Vertices = 4', 'Type = Not Equal To'. Now you'll see the Ngons (faces that have more than 4 edges) and probably some Tris (triangle faces) selected. You can now delete them or go and fix them one by one. Repeat this step until you can't see any Tris or Ngons selected.


Now you can try exporting your model into Unity. Hopefully this help :) otherwise, comment below and maybe post your Blend file online so I can check if anything is missing. Goodluck!